We already had this in the UK. All the drinks got reformulated, often without alternative, with cheap artificial sweeteners. If you like an occasional sugary drink hit you’re shit out of luck (except for classic coke at least).

The levy as outlined in the article, as @blind3rdeye@aussie.zone pointed out, is intended to be passed on to the consumer, with the price increase causing people to consume fewer sugary drinks. If they didn't pass it on, it would have no effect on dental health.

From the article:

Assuming a 20 per cent tax is passed on in full to consumers, the study predicted the price increase would result in a 24 per cent reduction in consumption.

However, there are ways you can design a policy like this to reduce the cost to consumers while still having an effect on dental health. In the UK, their levy is only applied to a drink "if it contains at least 5 grams (g) of sugar per 100 millilitres (ml) in its ready to drink or diluted form." As as result, the UK soft drink industry reformulated their drinks to fall below that amount (often by partially substituting non-sugar sweeteners) so that they wouldn't have to pay the tax at all and they wouldn't need to pass it on to consumers or absorb it.

From the article:

In 2018, the United Kingdom introduced a tax of 19.4 or 25.9 pence per litre, depending on the sugar content of beverages.

It led to a 46 per cent reduction in the sugar contained in soft drinks, the UK government said, with nearly 90 per cent of the market now containing sugar below the level at which the tax applies.

The study (https://bmjpublichealth.bmj.com/content/4/3/e002110) actually modelled the effect of reformulation, too:

To explore the impact of possible industry responses, we also modelled product reformulation scenarios with 50% and 100% sugar reductions (and no consumer response) and 50% and 80% pass through scenarios.

The health impact of the SSB tax is up to three times larger with 50% reformulation as compared with the base case and nearly five times with 100% reformulation.

Since the UK's policy has resulted in a 46% reformulation, we have a clear real-world template for bringing about a 50% reformulation and the health benefits that would accompany it.

I think passing it on to consumers is an assumed part of the idea; discouraging people from consuming drinks with added sugar, and thus discouraging companies from making and marketing such drinks.